Since, from the model of photons in circular motion
\(2\pi r=\lambda=\frac{c}{f}\) as \(f\) increases, \(r\) decreases.
And electrons are in orbit around the nucleus at radius \({r}_{e}\). Photons and the electrons are not interacting until \(r\) of the photons is comparable with \(r_e\) of the electrons orbits. At low \(f\) photons are in wide circular path, it hardly interact with orbit electrons at all. As \(f\) increases \(r\) decreases. When \(r\) nears \({r}_{e}\), photons begins to collide with electrons and electrons are ejected. The threshold effect can be a matter of geometry. And the frequency dependence of the emitted electrons' KE around \(r\) = \({r}_{e}\), is due to longer interaction time between the photon in its circular path and the electron in its orbit. This might be modeled as some linear function \(F(\frac{r_e}{r})\) for \(r\gt r_e\) and 1 for \(r \le r_e\), and that,
\(KE(f) = F(\frac{r_e}{r}).KE_{max}\) for \(r\gt r_e\)
since in circular at speed \(c\), \(c=r\omega=r.2\pi.f=\lambda . f\) then, \(\frac{1}{r}=\frac{2\pi.f}{c}\)
\(KE(f) = F(r_e.\frac{2\pi.f}{c}).KE_{max}\) for \(r\gt r_e\) that is to say
\(KE(f)\propto f\)
\(KE(f) = KE_{max}\) for \(r \le r_e\)
In this model however, when \(r\) equals \({r}_{e}\) the interaction should max out. That is to say, beyond certain value of \(f\) the KE of the electrons ejected no longer increases but saturates. Further increase in frequency results in the same photocurrent vs retarding voltage curve. Until it encounter the next electron orbit and is now interacting with two electron orbits. It is expected then, the ejected electrons have two distinct KEs. This effect should be seem as a split or bend at the stopping voltage intercept or a photocurrent vs retarding voltage graph. Unfortunately most presentations do not explain the bend in the graphs and often show only one of the split ends. The KE vs frequency curve should also then be stepwise instead of linear. Most however, assume that the electrons' KE increase linearly and don't investigate further.
A illustrative plot of Electron E_max vs Photon Frequency is shown below.
In this scenario, intensity of the incident radiation does not increase the energy of the ejected electrons either. Photons and electrons are likely to be paired interaction in that one photon collide with one electron, the latter being ejected. Intensity of a light beam is the average energy of many photons over an area per second. Increasing intensity without increasing the interaction time between one photon and one electron will not increase the KE of the ejected electrons.
If the energy of photons is a simple sum of its kinetic energies, rotational and translation, then
\({E}_{p}= \frac{1}{2}{m}_{p}c^2+\frac{1}{2}{m}_{p}c^2={m}_{p}c^2\)
which is a constant!
Base on this model, it is expected then, the ejected electrons have two or more distinct KEs as frequency increases. This effect should be seem as a split or bend at the stopping voltage intercept. Unfortunately most presentations do not explain the bend in the graphs and often show only one of the split ends.
An example of a split at the stopping voltage intercept is shown below. Highlighted are the corresponding consecutive electron shells on the red curve. A similar split also occurs on the blue curve.
Fodo and Fido, indeed.
